## new nth prime correct

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• Hello all: I send you a new formula (In MATHEMATICA) for the nth prime number L[1]=1; L[n_]:=L[n]=LCM[L[n-1],n] LG[n_]:=L[n]/L[n-1] FL[n_]:=Quotient[LG[n],n]
Message 1 of 1 , Apr 1, 2004
Hello all:

I send you a new formula (In MATHEMATICA) for the nth
prime number

L[1]=1;
L[n_]:=L[n]=LCM[L[n-1],n]
LG[n_]:=L[n]/L[n-1]
FL[n_]:=Quotient[LG[n],n]
Pii[n_ ]:=Sum[FL[i],{i,2,n}]
PrimeLCM[n_]:=
Floor[n*Log[n]]+Sum[1-Quotient[Pii[k],n],

{k,Floor[n*Log[n]],Floor[n*Log[n]+n*(Log[Log[n]]-1/2)+3]}]
Do[Print[n," ",Timing[PrimeLCM[n]]],{n,2,20,1}]

more fast than the previous:
www.primepuzzles.net problem 38

Te time of the previous formula is O(nlogn)^(3/2)
Which is the time of this new formula?

Sincerely

Sebastián Martín Ruiz
www.telefonica.net/c/smruiz

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